1) A researcher wishes to determine whether people with high blood pressure can
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1) A researcher wishes to determine whether people with high blood pressure can reduce their blood pressure by following a particular diet. Subjects were randomly assigned to either a treatment group or a control group. The sample mean and sample standard deviation of blood pressure was determined for each group, and a 95% confidence interval for the difference in the means for the treatment group versus the control group, i.e. µ(treatment) - µ(control), was found to be (-21, -6). Which of the following is correct?
a)We are 95% confident that the mean blood pressure of those who follow the diet is between 6 and 21 points higher than the average for those who do not follow the diet.
b)We are 95% confident that the mean blood pressure of those who follow the diet is between 6 and 21 points lower than the average for those who do not follow the diet.
c)The probability that the mean blood pressure for those on the diet is lower than for those not on the diet is 0.95.
d)The probability that the mean blood pressure for those on the diet is higher than for those not on the diet is 0.95.
e)Since all of the values in the confidence interval are less than 0, we are unable to conclude that there is a difference in blood pressure for those who follow the diet and those who do not.
2)In a controlled laboratory environment, a random sample of 10 adults and a random sample of 10 children were tested by a psychologist to determine the room temperature that each person finds most comfortable. The data are summarized below. Suppose that the psychologist decides to construct a 99% confidence interval for the difference in mean comfortable room temperatures instead of proceeding with a test of hypothesis. The 99% confidence interval turns out to be (-2.9, 3.1). Select the correct statement.
Sample Mean
Sample Variance
Adults
77.5
4.5
Children
74.5
2.5
a)It cannot be concluded at the 99% confidence level that there is actually a difference between the true mean comfortable room temperatures for the two groups.
b)It can be concluded at the 99% confidence level that the true mean room temperature for adults exceeds that for children.
c)It can be concluded at the 99% confidence level that the true mean comfortable room temperature for children exceeds that for adults.
d)The probability that the true mean difference in comfortable room temperature is between -2.9 and 3.1 is equal to 0.99.
3) Do motivation levels between Japanese and American managers differ? A randomly selected group of each were administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The SSATL scores are summarized below:
Sample Size
Sample Mean
Sample St. Dev.
American
173
77.4
11.1
Japanese
109
79.7
6.4
Given that the p-value is 0.03, which of the following is the appropriate conclusion?
a)At alpha=0.02, reject H0.
b)At alpha=0.025, reject H0.
c)At alpha=0.01, reject H0.
d)At alpha=0.025, fail to reject H0.
e)At alpha=0.05, fail to reject H0.
4) The non-parametric Wilcoxon Rank Sum test is not easily affected by outliers.
True
False
5)It is known that babies with low birthweight (less than 2500 grams) are at increased risk for a variety of health problems. The lowbwt1.sas7bdat dataset contains data from 65 mothers, some of whom had babies with low birthweight. It has been hypothesized that smoking may be a risk factor for having babies with low birthweight. In this dataset the BWT variable measures the birthweight of babies in grams, while the mother’s smoking status is encoded in the SMOKE variable (SMOKE = 0 for non-smokers, SMOKE = 1 for smokers).
a) Specify the null hypothesis, and identify the parameters of interest.
Sample Mean
Sample Variance
Adults
77.5
4.5
Children
74.5
2.5
Explanation / Answer
b) We are 95% confident that the mean blood pressure of those who follow the diet is between 6 and 21 points lower than the average for those who do not follow the diet.
Explanation- 95% CI of µ(treatment) - µ(control) is (-21, -6). It means treatment lowering the blood pressure compared to control diet. which is between 6 and 21. The negative sign of the confidence interval indicates that the treatment is lowering the blood pressure.
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